Effect of the actions do not appear immediately - the behaviour evolves with time
Eg. To go from 30 km/hr to 60 km/hr in a car we press the accelerator pedal. We know the card doesn't reach 60 km/hr immedately, it takes a few seconds to accelerate to that velocity.
Mathematical Representation of a physical, biological or information system. In this class, we focus on dynamical systems (mostly in state-space form)
"All models are wrong, but some are useful". Often, a model is an approximation of the real system. The real system might be too complicated to model perfectly. For eg. aerodynamic interactions between the rotor blades of a quadcopter, friction between the tire and ground for a physical robot etc.
The required modelling accuracy depends on the application at hand. Eg. aerodynamic drag can be neglected for low-speed control design for quadcopters
Analysis and design must performed keeping in mind the limitations of the model
Simulation
Controller design
Verfication and Validaton
Diagnostics, predictive maintenance
Linear models are convenient becuase they're well understood. Lots of tools and techniques are available for the analysis, simulatios, synthesis, simulation, verification etc linear systems. Unfortunately, real world physical systems are never exactly linear. But the behaviour around the desired operating points can be approximated with a linearized version of the actual non-linear modle. Eg. for a quadcopter, the behaviour near hoover condtion can be approximated with linear systems
Equation is:
\[ \tau\dot{x} + x = u(t) \]where \(\tau\) is the time constant. The output reaches around 63% of its steady state value with time \(\tau\).